Hybrid State-space Model and Adjusting Procedure Based on Bayesian Approaches for Spatio-temporal Rainfall Disaggregation Suci Astutik PhD Student, Statistics Department, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia; Mathematics Department, Brawijaya University, Malang, Indonesia suci_sp@yahoo.com ; suci_sp@mhs.statistika.its.ac.id Nur Iriawan, Suhartono, Sutikno Statistics Department, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia nur_i@statistika.its.ac.id ; suhartono@statistika.its.ac.id ; sutikno@statistika.its.ac.id Abstract— Disaggregation is the transforming process from high- level scale data into low-level which preserves the consistency of the high-level statistic characteristics. This process, considering the dependence between spatial and temporal, is known as the spatio-temporal disaggregation. In general, this method is divided into two stages, namely the data modeling and preserving of consistency the high level scale statistic characteristics. This study proposes a hybrid model that combines a state-space model and adjusting procedure to disaggregate spatio-temporal rainfall through Bayesian approach using WinBUGS. The results show that the generated hourly rainfall data are consistent with the observed daily rainfall data at some locations which have only the daily rainfall data in the watershed Sampean, Bondowoso, Indonesia. Keywords-component; adjusting procedure, Bayesian, rainfall, spatio-temporal disaggregation, state-space model I. INTRODUCTION Disaggregation method is a procedure that transforms the high level time scale to the low level time scale which preserves their consistency [1], [2]. This method can be used to overcome the limited availability on the low of the high level time scale data. Generally, there are two stages of disaggregation method, namely modeling of the observed low level data in sample locations and preserving characteristics of the observed high level data to the predicted/generated low level data of unsampled locations. A spatio-temporal disaggregation method is a method that involves a spatio-temporal dependence. This methods are applied to obtain rainfall time series at the low level from the high level time scale on some locations. In the previous research, Koutsoyiannis [2] has developed the spatio-temporal rainfall disaggregation modeling, which extends AR(1) model to Multivariate Autoregressive, MAR(1), model at several locations. This development has succeeded employing the correlation among sites in the model, and combining the Bartlett Lewis rainfall model and adjusting procedure (coupling transformation) in a MUDRAIN package software. This disaggregation method has been applied at Brue, South- Western England and Tyber river Basin, Italy [3], [4]. Meanwhile, the Bayesian approach have been widely used in statistical modeling. The main advantages of this method is its ability to create prediction accurately, especially for the sparse data [5]. It can also overcome the case with missing value and the complex hierarchical structure model. Its ability to incorporate prior knowledge without limiting assumptions of classical distribution, has made Bayesian inference to be more powerful as prediction tool for many fields [5]. On the other hand, in the rainfall studies, Bayesian approach is used to predict frequency of rainfall event, duration, and rainfall intensity [6], [7] and tackle the difficulty in estimating many parameters in the temporal disaggregation model [8]. Furthermore, Makhnin [9] employed the Gibbs sampler in developing a Bayesian approach applied in state space (dynamic) linear model for generating occurrence and intensity rainfall in daily periods together. The same approach was used by Sigrist [10] to model three-hourly rain data in Switzerland. The last two approaches can overcome a negative value, under estimation on autocorrelation and cross correlation lag 1 in the model, especially when there are no rain. In addition, these last two approaches involve only fewer parameters. These approaches, however, have difficulty in creating synthetic rainfall in the dense grid of locations (regionalization), and can not generate lower time scale data from higher scale time data yet. The main purpose of this study is to produce the rainfall depth in the low of observed high level time scale in the other locations by using disaggregation method. Our interest of this method is focused on the hybrid of state space model and adjusting procedure. The method would be employed here to disaggregate the observed daily (high level time scale) spatio- temporal rainfall depth to the synthetic hourly (low level time scale) rainfall depth in other locations. The state-space model is to form model of the observed low level data by using